A convenience store has two separate locations where customers can be checked out as they leave. These locations each have two cash registers and two employees who check out customers. Let X be the number of cash registers being used at a particular time for location 1 and Y the number being used at the same time for location 2. The joint probability function is given by y x 012 0 0.12 0.04 0.04 1 0.08 0.19 0.05 2 0.06 0.12 0.30 (a) Give the marginal density of both X and Y as well as the probability distribution of X given Y